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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-6

  • question_answer
    If S is the sample space and \[\mathbf{P}\left( A \right)=\frac{1}{3}\mathbf{P}\left( B \right)\]and \[\mathbf{S}=\mathbf{A}\cup \mathbf{B}\], where A and B are two mutually exclusive events, then \[\mathbf{P}\left( A \right)=\]

    A)  \[\frac{1}{3}\]                         

    B)  \[\frac{1}{4}\]              

    C)  \[\frac{1}{2}\]                         

    D)  \[\frac{2}{3}\]

    Correct Answer: B

    Solution :

    [b] \[\because A\And B\]be mutually exclusive events \[\And S=A\cup B.\] \[\therefore ~P\left( A\cup B \right)=P\left( A \right)+P\left( B \right)\] \[\Rightarrow P\left( S \right)=\frac{1}{3}.P\left( B \right)+P\left( B \right)\]        \[\Rightarrow 1=\frac{4}{3}.P(B)\] \[\Rightarrow P(B)=\frac{4}{3}\] \[\therefore p(A)=\frac{1}{3}.p(B)=\frac{1}{3}.\frac{1}{4}=\frac{1}{4}\] Hence, option [b] is correct.


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